Analytical properties of distribution functions for relative velocities of molecules in a shock-compressed binary mixture of gases

Abstract

Aim: to analytically investigate the existence or absence of the effect of overlapping values of distribution functions for relative velocities of molecules in a shock-compressed binary mixture of gases.

Methodology. Asymptotic and approximation methods of mathematical physics were used.

Results. It is analytically shown that in the modified bimodal model of a shock-compressed binary mixture of gases, there are effects of overlapping distribution functions with respect to the relative velocities of molecules. These effects, consisting in an excess of the amounts of energetically active molecules overcoming the threshold of barrier processes inside the wave front compared with a similar amount beyond it, can occur in a wide range of molecular weights and concentrations in a shock-compressed binary mixture of gases.

Research implications. The obtained analytical results are essential for clarifying the issue of the need to take into account translational disequilibrium when determining the velocity coefficients of energetically activated inelastic collisions inside shock wave fronts.